# How do you factor -x^2+3x+4?

Apr 5, 2018

See a solution process below:

#### Explanation:

Because the ${x}^{2}$ coefficient is $- 1$ we know the coefficient for one the $x$ terms in the factor will also be $1$ and the other a $- 1$:

$\left(x\right) \left(- x\right)$

Because the constant is a positive and the coefficient for the $x$ term is a positive, then the sign for the constants in the factors will both be positive::

$\left(x +\right) \left(- x +\right)$

Now we need to determine the factors which multiply to 4 and also add to 3:

$1 \times 4 = 4$; $- 1 + 4 = 3$ <- this IS the factor

$\left(x + 1\right) \left(- x + 4\right)$